Brownian motion with time-dependent friction and single-particle dynamics in liquids

TL;DR

This paper extends a microscopic theory of molecular motion in liquids by incorporating time-dependent friction into a non-Markovian Langevin framework, successfully describing atomic diffusion across various liquids and densities.

Contribution

It introduces a self-consistent, time-dependent friction model into Brownian dynamics, improving understanding of atomic motion in liquids with variable density.

Findings

Velocity autocorrelation functions match experimental data across liquids.

Friction decays exponentially at low densities, increases exponentially at high densities.

The model offers a new perspective on atomic dynamics in liquids.

Abstract

A microscopic theory of molecular motion in classical monatomic liquids, proposed by Glass and Rice [Phy. Rev. 176, 239 (1968)], is revisited and extended to incorporate the dynamic friction in the Brownian description of the atomic diffusion in a mean-time-dependent harmonic force field. A modified, non-Markovian Langevin equation is utilized to derive an equation of motion for the velocity autocorrelation function with time-dependent friction coefficient. Numerical solution of the equation gives an excellent account of the velocity autocorrelation function in LJ liquids, liquid alkali and transition metals over a broad range of density and temperature. Derivation of the equation of motion leads to a self-consistent expression for the time-dependence of friction coefficient. Our results demonstrate that the nature of time-dependence of the friction coefficient changes dramatically with the liquid density. At low and moderate densities, the dynamic friction decays exponentially whereas it increases exponentially at high liquid densities. Our findings provide an opportunity to have a new outlook of the Brownian description of atomic dynamics in liquids.